We are going to stay in Jackson Hole (flying in here) and then going to West Yellowstone. Where should we fly out of after West Yellowstone?
Check flying out of Bozeman. Or Billings, Idaho Falls or back to Jackson.
You will need to check if there is a big drop-off fee for the rental car to decide if it is worthwhile to fly out of another city or to return to Jackson. I'd also encourage you to try and get lodging inside both parks if you can as the distances are long and the speeds slow with plenty of opportunities to stop or be stopped by animal jams on the highways. I've also seen long lines backed up at the entrance to Yellowstone and you don't want to waste your precious time watching the car ahead of you.
West Yellowstone also has a seasonal airport. When is your trip?